Division and Percentages:

Calculating Percentages

Percent means “out of 100,” but we aren’t always working with a set of 100 things. We can still calculate the percentage by taking the amount we have divided by the total amount.

Video Source (07:01 mins) | Transcript

Example:

What percentage is 2 hours of a day?

Answer: There are 24 hours in a day, so the total amount we are comparing to is 24. To calculate the percentage we divide 2 by 24.

Amount ÷ Total Amount = 2 ÷ 24 = 0.08333...

Then change the decimal into a percentage by multiplying by 100 and adding a % symbol.

0.083333… = 8.3% (rounded to the nearest tenth)

Here are the things to remember from this lesson:

When finding the percent: amount ÷ total amount
When changing decimal to a percent: multiply by 100 and add a % symbol.

Practice Problems

What percentage is 24 minutes out of an hour?
You are on a trip that is 292 km long. So far you have driven 88 km. What percentage of the trip have you traveled? (Round to the nearest whole percentage.)
This month you spent $178 on food. Your total budget for the month is $1200. What percentage of the budget was spent on food? (Round to the nearest whole percentage.)
You make and sell bread. The flour costs $53 a week. The cost of all your ingredients is $84 a week. What percentage of your cost is the flour? (Round to the nearest whole percentage.)
You take a test and get some of the extra credit points correct. You get 22 points out of 20 possible points. What is your percentage on the test?
A water tank holds 75L of water. There are currently 27L in the tank. What percent of the tank is empty? (Hint: $75-27$ is the amount missing. What percent is missing?)

Solutions

40%
(24 ÷ 60 = 0.4 = 40%)

30%
(88 ÷ 292 = 0.30137 = 30%) (Written Solution)

To find a percentage we calculate

Amount ÷ Total Amount

The amount driven so far is 88 km. The total length of the trip is 292 km.

$\frac{\text{Amount}}{{\text{Total}} \, {\text{amount}}} = \frac{88}{292} = 0.30137...$

Next, we must take this decimal and change it to a percentage. To do this we multiply by 100 or move the decimal to the right two places and then include a % symbol.

0.30137…= 30.137%

Finally, round to the nearest whole percentage.

Since there is a 1 in the tenths place we don’t round up.

Final answer: 30%

15%
(178 ÷ 1200 = 0.14833... = 15%)

63%
(53 ÷ 84 = 0.6309… = 63%)

110%
22 ÷ 20 = 1.1 = 110%

64%
((75-27) ÷ 75 = 48 ÷ 75 = 0.64 = 64%) (Written Solution)

We are looking for the percentage of water missing from the tank. Calculate this by first finding the amount of water missing. $75-27=48$

Next, calculate

$\frac{\text{Amount}}{{\text{Total}} \, {\text{amount}}} = \frac{48}{75} = 0.64$

Note: Things written in fraction form also mean division. $\frac{48}{75}$ = 48 ÷ 75.

Finally, change the decimal into a percentage by multiplying by 100 and adding the % symbol. This is the same as moving the decimal two places to the right and adding the % symbol..

Final answer: 0.64=64%